Multiple Blender processes for multiple GPUs?
It turns out all I needed was to update the NVIDIA driver to v346.72 for the ASUS GTX 970 Strix cards to be able to handle multiple processes in tandem.

Update - Oct 2019

To those wondering if there was a performance gain in doing this: yes, there was. 

I don't have the specifics with me as this was done a few years back, but I do remember the render times breaking down like this simplified example: 

1 GPU renders 1 frame of an animation in 4 minutes, so in theory bulking up to 4 GPUs should render that one frame in 1 minute. This wasn't what I was seeing in reality though. The actual result took more like 1.2 minutes per frame.

So for a 200 frame animation, the math broke down like this:

All 4 GPUs working as one:


(200 frames / 1 Combined GPU) = 200 frames * 1.2 minutes per frame = 240 mins total


Splitting up the GPUs to independently work on a queue of frames:


(200 frames / 4 GPUs) = 50 frames per GPU * 4 minutes per frame in parallel = 200 mins total